{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction: Bayesian Optimization using Hyperopt\n",
    "\n",
    "In this notebook we will walk through the basics of [Bayesian Model-Based Optimization](https://sigopt.com/static/pdf/SigOpt_Bayesian_Optimization_Primer.pdf) using [Hyperopt](https://jaberg.github.io/hyperopt/) to find the minimum of a function. After we are familiar with the basic concepts, we can use these powerful methods to solve many problems, inlcuding [hyperparamter optimization](https://en.wikipedia.org/wiki/Hyperparameter_optimization) of machine learning models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Model-Based Optimization Primer\n",
    "\n",
    "There are four parts to an optimization problem:\n",
    "\n",
    "1. Objective function: what we want to minimize\n",
    "2. Domain space: values of the parameters over which to minimize the objective\n",
    "3. Hyperparameter optimization function: constructs the surrogate function and chooses next values to evaluate\n",
    "4. Trials: score, parameter pairs recorded each time we evaluate the objective function\n",
    "\n",
    "Evaluating the objective function is the expensive part of optimization, so ideally we want to limit calls to this function. One way we can limit calls is by choosing the next values to try in the objective function based on the past results. \n",
    "Bayesian optimization differs from random or grid search by doing exactly this: rather than just selecting from a grid __uninformed__ by past objective function evaluations, Bayesian methods take into account the previous results to try more promising values. They work by constructing a probability model of the objective function (called a surrogate function) $p(\\text{score} | \\text{parameters}$ which is much easier to optimize than the actual objective function. \n",
    "\n",
    "After each evaluation of the objective function, the algorithm updates the probability model (usually given as $p(y | x)$ incorporating the new results. [Sequential Model-Based Optimization (SMBO) methods are a formalization of Bayesian optimization](https://towardsdatascience.com/a-conceptual-explanation-of-bayesian-model-based-hyperparameter-optimization-for-machine-learning-b8172278050f) that update the probability model sequentially: every evaluation of the objective function with a set of values updates the model with the idea that eventually the model will come to represent the true objective function. This is an application of Bayesian Reasoning. The algorithm forms an initial idea of the objective function and updates it with each new piece of evidence.\n",
    "\n",
    "The next values to try in the objective function are selected by the algorithm optmizing the probability model (surrogate function) usually with a criteria known as Expected Improvement. Finding the values that will yield the greatest expected improvement in the surrogate function is much cheaper than evaluating the objective function itself. By choosing the next values based on a model rather than randomly, the hope is that the algorithm with converge to the true best values much quicker. The overall goal is to evaluate the objective function fewer times by spending a little more time choosing the next values. Overall, Bayesian Optimization and SMBO methods:\n",
    "\n",
    "* Converge to a lower score of the objective function than random search\n",
    "* Require far less time to find the optimum of the objective function\n",
    "\n",
    "So, we get both faster optimization and a better result. These are both two desirable outcomes especially when we are working with hyperparameter tuning of machine learning models! \n",
    "\n",
    "### Sequential Model Based Optimization using the Tree Parzen Estimator\n",
    "\n",
    "SMBO methods differ in part 3, the algorithm used to construct the probability model (also called the Surrogate Function). Several options are for the surrogate function are:\n",
    "\n",
    "* Gaussian Processes\n",
    "* Tree-structured Parzen Estimator\n",
    "* Random Forest Regression\n",
    "\n",
    "Hyperopt implements the Tree-strucuted Parzen Estimator. The details of this algorithm are not that complicated, but we will not discuss them in this notebook (for details refer to [this article.]) We don't need to worry about implementing the algorithm because Hyperopt takes care of that for us. We just have to make sure we have properly defined the __objective function__ and the __domain of values to search over__. Then, we select the algorithm and let it run. Hyperopt will automatically keep track of past results to inform the model (part 4.) but we can also use a custom object to get more information about the optimization procedure. \n",
    "\n",
    "## Hyperopt\n",
    "\n",
    "Hyperopt is an open-source Python library for Bayesian optimization that implements SMBO using the Tree-structured Parzen Estimator. There are a number of libraries available for Bayesian optimization and Hyperopt differs in that it is the only one to currently offer the Tree Parzen Estimator. Other libraries use a Gaussian Process or a Random Forest regression for the surrogate function (probability model). \n",
    "\n",
    "In this notebook, we will implement both random search (Hyperopt has a method for this) as well as the Tree Parzen Estimator, a Sequential Model-Based Optimization method. We will use a simple problem that will allow us to learn the basics as well as a number of techniques that will be very helpful when we get to more complex use cases. With all that out of the way, let's get started with Hyperopt! \n",
    "\n",
    "#### Resources\n",
    "\n",
    "For more details on Bayesian Model Based Optimization, here are some good articles:\n",
    "\n",
    "* Algorithms for Hyper-Parameter Optimization [Link](https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf)\n",
    "* Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures [Link](http://proceedings.mlr.press/v28/bergstra13.pdf)\n",
    "* Bayesian Optimization Primer [Link](https://sigopt.com/static/pdf/SigOpt_Bayesian_Optimization_Primer.pdf)\n",
    "* Taking the Human Out of the Loop: A Review of Bayesian Optimization [Link](https://www.cs.ox.ac.uk/people/nando.defreitas/publications/BayesOptLoop.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Good old pandas and numpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Unfortunately I'm still using matplotlib for graphs\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Objective\n",
    "\n",
    "\n",
    "For our objective function, we will use a simple polynomial function with the goal being to find the minimu value. This function has one global minimum over the range we define it as well as one local minimum.\n",
    "\n",
    "When we define the objective function, we must make sure it returns a single real-value number to _minimize_. If we use a metric such as accuracy, then we would have to return the _negative_ of accuracy to tell our model to find a better accuracy! We can also return a dictionary (we will see this later) where one of the keys must be \"loss\". Here we will just return the output of the function $f(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(x):\n",
    "    \"\"\"Objective function to minimize\"\"\"\n",
    "    \n",
    "    # Create the polynomial object\n",
    "    f = np.poly1d([1, -2, -28, 28, 12, -26, 100])\n",
    "\n",
    "    # Return the value of the polynomial\n",
    "    return f(x) * 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum of -219.8012 occurs at 4.8779\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0eea06eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Space over which to evluate the function is -4 to 5\n",
    "x = np.linspace(-5, 6, 10000)\n",
    "y = objective(x)\n",
    "\n",
    "miny = min(y)\n",
    "minx = x[np.argmin(y)]\n",
    "\n",
    "# Visualize the function\n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.style.use('fivethirtyeight')\n",
    "plt.title('Objective Function'); plt.xlabel('x'); plt.ylabel('f(x)')\n",
    "plt.vlines(minx, min(y)- 50, max(y), linestyles = '--', colors = 'r')\n",
    "plt.plot(x, y);\n",
    "\n",
    "# Print out the minimum of the function and value\n",
    "print('Minimum of %0.4f occurs at %0.4f' % (miny, minx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Domain\n",
    "\n",
    "The domain is the values of x over which we evaluate the function. First we can use a uniform distribution over the space our function is defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyperopt import hp\n",
    "\n",
    "# Create the domain space\n",
    "space = hp.uniform('x', -4, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can draw samples from the space using a Hyperopt utility. This is useful for visualizing a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ef19e828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from hyperopt.pyll.stochastic import sample\n",
    "\n",
    "\n",
    "samples = []\n",
    "\n",
    "# Sample 10000 values from the range\n",
    "for _ in range(10000):\n",
    "    samples.append(sample(space))\n",
    "    \n",
    "\n",
    "# Histogram of the values\n",
    "plt.hist(samples, bins = 20, edgecolor = 'black'); \n",
    "plt.xlabel('x'); plt.ylabel('Frequency'); plt.title('Domain Space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When running, our algorithm will sample values from this distribution, initially at random as it explores the domain space, but then over time, it will \"focus\" on the most promising values. Therefore, the algorithm should more values around 4.9, the minimum of the function. We can compare this to random search which should try values evenly from the entire distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyperparameter Optimization Algorithm\n",
    "\n",
    "There are two choices for a hyperparameter optimization algorithm in Hyperopt: random and Tree Parzen Estimator. We can use both and compare the results. Using the `suggest` algorithm in these families automatically configures the algorithm for us. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyperopt import rand, tpe\n",
    "\n",
    "# Create the algorithms\n",
    "tpe_algo = tpe.suggest\n",
    "rand_algo = rand.suggest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# History\n",
    "\n",
    "Storing the history is as simple as making a `Trials` object that we pass into the function call. This is not strictly necessary, but it gives us information that we can use to understand what the algorithm is doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyperopt import Trials\n",
    "\n",
    "# Create two trials objects\n",
    "tpe_trials = Trials()\n",
    "rand_trials = Trials()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run the Optimization\n",
    "\n",
    "Now that all four parts are in place, we are ready to minimize! Let's do 2000 runs of the minimization with both the random algorithm and the Tree Parzen Estimator algorithm. \n",
    "\n",
    "The `fmin` function takes in exactly the four parts specified above as well as the maximum number of evaluations to run. We will also set a `rstate` for reproducible results across multiple runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyperopt import fmin\n",
    "\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "tpe_best = fmin(fn=objective, space=space, algo=tpe_algo, trials=tpe_trials, \n",
    "                max_evals=2000, rstate= np.random.RandomState(80))\n",
    "\n",
    "# Run 2000 evals with the random algorithm\n",
    "rand_best = fmin(fn=objective, space=space, algo=rand_algo, trials=rand_trials, \n",
    "                 max_evals=2000, rstate= np.random.RandomState(80))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum loss attained with TPE:    -219.8012\n",
      "Minimum loss attained with random: -219.8012\n",
      "Actual minimum of f(x):            -219.8012\n",
      "\n",
      "Number of trials needed to attain minimum with TPE:    859\n",
      "Number of trials needed to attain minimum with random: 1713\n",
      "\n",
      "Best value of x from TPE:    4.8782\n",
      "Best value of x from random: 4.8782\n",
      "Actual best value of x:      4.8779\n"
     ]
    }
   ],
   "source": [
    "# Print out information about losses\n",
    "print('Minimum loss attained with TPE:    {:.4f}'.format(tpe_trials.best_trial['result']['loss']))\n",
    "print('Minimum loss attained with random: {:.4f}'.format(rand_trials.best_trial['result']['loss']))\n",
    "print('Actual minimum of f(x):            {:.4f}'.format(miny))\n",
    "\n",
    "# Print out information about number of trials\n",
    "print('\\nNumber of trials needed to attain minimum with TPE:    {}'.format(tpe_trials.best_trial['misc']['idxs']['x'][0]))\n",
    "print('Number of trials needed to attain minimum with random: {}'.format(rand_trials.best_trial['misc']['idxs']['x'][0]))\n",
    "\n",
    "# Print out information about value of x\n",
    "print('\\nBest value of x from TPE:    {:.4f}'.format(tpe_best['x']))\n",
    "print('Best value of x from random: {:.4f}'.format(rand_best['x']))\n",
    "print('Actual best value of x:      {:.4f}'.format(minx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Tree Parzen estimator and random search found the exact same minimum of the function to 4 decimal places. Sometimes even random search gets lucky (especially when we run it for so many iterations. However, we can see that TPE found the minimum in about half the number of iterations. After finding this minimum, we could have stopped running the algorith!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if there is any difference in time between the two methods. We can use the built in Jupyter magic command for timing (running the function 3 times)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "519 ms ± 78.3 ms per loop (mean ± std. dev. of 7 runs, 3 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 3\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "best = fmin(fn=objective, space=space, algo=tpe_algo, max_evals=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "91.5 ms ± 7.74 ms per loop (mean ± std. dev. of 7 runs, 3 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 3\n",
    "\n",
    "# Run 2000 evals with the random algorithm\n",
    "best = fmin(fn=objective, space=space, algo=rand_algo, max_evals=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a point of interest, the random algorithm ran about 5 times faster than the tpe algorithm. This shows that the TPE method is taking more time to propose the next set of parameters while the random method is just choosing from the space well, randomly. The extra time to choose the next parmaeters is made up for by choosing better parameters that should let us make fewer overall calls to the objective function (which is the most expensive part of optimization). Here we ran the same number of totals calls, but this was probably not necessary because the Tree Parzen Estimator will converge on the optimum quickly without the need for more iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Results\n",
    "\n",
    "We see that both models returned values very close to the optimal. To see how they differ in the search procedure, we can take a look at the trials objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loss</th>\n",
       "      <th>iteration</th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-70.221046</td>\n",
       "      <td>0</td>\n",
       "      <td>3.159530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.255827</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.188930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-27.994579</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.237837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-101.663418</td>\n",
       "      <td>3</td>\n",
       "      <td>3.488275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-42.851011</td>\n",
       "      <td>4</td>\n",
       "      <td>2.807139</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         loss  iteration         x\n",
       "0  -70.221046          0  3.159530\n",
       "1    5.255827          1 -0.188930\n",
       "2  -27.994579          2 -2.237837\n",
       "3 -101.663418          3  3.488275\n",
       "4  -42.851011          4  2.807139"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tpe_results = pd.DataFrame({'loss': [x['loss'] for x in tpe_trials.results], 'iteration': tpe_trials.idxs_vals[0]['x'],\n",
    "                            'x': tpe_trials.idxs_vals[1]['x']})\n",
    "                            \n",
    "tpe_results.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extracting these results was a little work. We could have formatted the objective function to return more useful information (in a little bit we'll how to do this)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we can plot the values that were evaluated over time. As the algorithm progresses, these should tend to cluster around the actual best value (near 4.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ef1c3438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tpe_results['iteration'], tpe_results['x'],  'bo', alpha = 0.4);\n",
    "plt.xlabel('iteration'); plt.ylabel('x value'); plt.title('TPE Sequence of Evaluations');\n",
    "plt.hlines(minx, 0, 2000, linestyles = '--', colors = 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that over time, the algorithm tended to try values closer to 4.9. The local minimum around -4 likely threw off the algorithm initially, but the points tend to cluster around the actual minimum as the algorithm progresses. \n",
    "\n",
    "We can also plot the histogram to see the distribution of values tried."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0ef2365c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(tpe_results['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of TPE Values'); plt.xlabel('Value of x'); plt.ylabel('Count');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sure enough, the algorithm tried many values closer to 4.9 that anywhere else! This clearly shows the benefits of choosing the next values based on the past values: more evaluations of promising values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Loss of -219.8012 occured at iteration 859\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0eeb26198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sort with best loss first\n",
    "tpe_results = tpe_results.sort_values('loss', ascending = True).reset_index()\n",
    "\n",
    "plt.plot(tpe_results['iteration'], tpe_results['loss'], 'bo');\n",
    "plt.xlabel('iteration'); plt.ylabel('loss'); plt.title('TPE Sequence of Losses');\n",
    "\n",
    "print('Best Loss of {:.4f} occured at iteration {}'.format(tpe_results['loss'][0], tpe_results['iteration'][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Results\n",
    "\n",
    "We should contrast the TPE results with those from random search. Here we do not expect to see any trend in values evaluated over time because the values are selected randomly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loss</th>\n",
       "      <th>iteration</th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-70.221046</td>\n",
       "      <td>0</td>\n",
       "      <td>3.159530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.255827</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.188930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-27.994579</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.237837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-101.663418</td>\n",
       "      <td>3</td>\n",
       "      <td>3.488275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-42.851011</td>\n",
       "      <td>4</td>\n",
       "      <td>2.807139</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         loss  iteration         x\n",
       "0  -70.221046          0  3.159530\n",
       "1    5.255827          1 -0.188930\n",
       "2  -27.994579          2 -2.237837\n",
       "3 -101.663418          3  3.488275\n",
       "4  -42.851011          4  2.807139"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand_results = pd.DataFrame({'loss': [x['loss'] for x in rand_trials.results], 'iteration': rand_trials.idxs_vals[0]['x'],\n",
    "                            'x': rand_trials.idxs_vals[1]['x']})\n",
    "                            \n",
    "rand_results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0efaa4470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rand_results['iteration'], rand_results['x'],  'bo', alpha = 0.4);\n",
    "plt.xlabel('iteration'); plt.ylabel('x value'); plt.title('rand Sequence of Evaluations');\n",
    "plt.hlines(minx, 0, 2000, linestyles = '--', colors = 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, the random algorithm is just \"randomly\" choosing the next set of values to try! There is no logical order here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Loss of -219.8012 occured at iteration 1713\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0efa405f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sort with best loss first\n",
    "rand_results = rand_results.sort_values('loss', ascending = True).reset_index()\n",
    "\n",
    "plt.hist(rand_results['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of Random Values'); plt.xlabel('Value of x'); plt.ylabel('Count');\n",
    "\n",
    "# Print information\n",
    "print('Best Loss of {:.4f} occured at iteration {}'.format(rand_results['loss'][0], rand_results['iteration'][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, there is no discernable clustering because this method is choosing the next values randomly. In this case, it happended across the minimum of the function because it was a relatively simple problem and we used many iterations. This would not likely be the case when we are optimizing more complex functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Slightly Advanced Concepts\n",
    "\n",
    "These probably should not be called advanced but smarter concepts because they will make our jobs easier. We will cover two upgrades we can make:\n",
    "\n",
    "* Smarter domain space over which to search\n",
    "* Return more useful information from the objective function\n",
    "\n",
    "These will be helpful when it comes time for hyperparameter optimization. Master the details on the easy problems so you can use the tools more effectively on the difficult problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Better Domain Space\n",
    "\n",
    "In this problem, we can cheat because we know where the minimum is and therefore can define a region of higher probability around this value of x. In more complicated problems, we don't have a graph to show us the minimum, but we can still use experience and knowledge to inform our choice of a domain space. \n",
    "\n",
    "Here we will make a normally distributed domain space around the value where the minimum of the objective function occurs, around 4.9. This is simple to do in Hyperopt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normally distributed space\n",
    "space = hp.normal('x', 4.9, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0eeb70780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = []\n",
    "\n",
    "# Sample 10000 values from the range\n",
    "for _ in range(10000):\n",
    "    samples.append(sample(space))\n",
    "    \n",
    "\n",
    "# Histogram of the values\n",
    "plt.hist(samples, bins = 20, edgecolor = 'black'); \n",
    "plt.xlabel('x'); plt.ylabel('Frequency'); plt.title('Domain Space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much closer to the true value! This would help both the random search and the TPE find the minimum quicker (for random search it would help because we are concentrating the possible values around the optimum)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Useful Trials Object\n",
    "\n",
    "Another modification to make is to return more useful information from the objective function. We do this using a dictionary with any information we want included. The only requirements are that the dictionary must contain a single real-valued metric to minimize stored under a `\"loss\"` key and whether the function sucessfully ran, stored under a `\"status\"` key. Here we make the modifications to the objective to store the value of x as well as the time to evaluate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hyperopt import STATUS_OK\n",
    "from timeit import default_timer as timer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(x):\n",
    "    \"\"\"Objective function to minimize with smarter return values\"\"\"\n",
    "    \n",
    "    # Create the polynomial object\n",
    "    f = np.poly1d([1, -2, -28, 28, 12, -26, 100])\n",
    "\n",
    "    # Evaluate the function\n",
    "    start = timer()\n",
    "    loss = f(x) * 0.05\n",
    "    end = timer()\n",
    "    \n",
    "    # Calculate time to evaluate\n",
    "    time_elapsed = end - start\n",
    "    \n",
    "    results = {'loss': loss, 'status': STATUS_OK, 'x': x, 'time': time_elapsed}\n",
    "    \n",
    "    # Return dictionary\n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run the algorithm the same as before. We'll create a new `Trials` object to save new results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# New trials object\n",
    "trials = Trials()\n",
    "\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "best = fmin(fn=objective, space=space, algo=tpe_algo, trials=trials, \n",
    "                max_evals=2000, rstate= np.random.RandomState(120))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time our trials object will have all of our information in the `results` attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'loss': -189.3682041842684,\n",
       "  'status': 'ok',\n",
       "  'time': 3.185775059222351e-05,\n",
       "  'x': 5.312379584994148},\n",
       " {'loss': -219.325099632915,\n",
       "  'status': 'ok',\n",
       "  'time': 2.3893312944167633e-05,\n",
       "  'x': 4.8166084516702705}]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = trials.results\n",
    "results[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we have more information from the results. We can extract the results into a dataframe for inspect and plotting if we like. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>loss</th>\n",
       "      <th>x</th>\n",
       "      <th>iteration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>956</th>\n",
       "      <td>0.000022</td>\n",
       "      <td>-219.801204</td>\n",
       "      <td>4.878152</td>\n",
       "      <td>956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1316</th>\n",
       "      <td>0.000029</td>\n",
       "      <td>-219.801204</td>\n",
       "      <td>4.878111</td>\n",
       "      <td>1316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>402</th>\n",
       "      <td>0.000023</td>\n",
       "      <td>-219.801204</td>\n",
       "      <td>4.878189</td>\n",
       "      <td>402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>914</th>\n",
       "      <td>0.000023</td>\n",
       "      <td>-219.801203</td>\n",
       "      <td>4.878064</td>\n",
       "      <td>914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1954</th>\n",
       "      <td>0.000044</td>\n",
       "      <td>-219.801203</td>\n",
       "      <td>4.878222</td>\n",
       "      <td>1954</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          time        loss         x  iteration\n",
       "956   0.000022 -219.801204  4.878152        956\n",
       "1316  0.000029 -219.801204  4.878111       1316\n",
       "402   0.000023 -219.801204  4.878189        402\n",
       "914   0.000023 -219.801203  4.878064        914\n",
       "1954  0.000044 -219.801203  4.878222       1954"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Results into a dataframe\n",
    "results_df = pd.DataFrame({'time': [x['time'] for x in results], \n",
    "                           'loss': [x['loss'] for x in results],\n",
    "                           'x': [x['x'] for x in results],\n",
    "                            'iteration': list(range(len(results)))})\n",
    "\n",
    "# Sort with lowest loss on top\n",
    "results_df = results_df.sort_values('loss', ascending = True)\n",
    "results_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was a simple optimization problem, so the lowest score obtained does not really differ from that with the uniform distribution. It took around the same number of iterations to converge. We can compare the distribution though to see if better values were tried."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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//1t17rE6fH19ERYWppot+fv7lzv+BgYGGD9+PFavXg13d3d4eXnh0aNHOHbsGO7evYs+ffpUe4n6o48+wtq1a7F8+XKcPXsWnTp1wh9//IGDBw9iyJAhiI+P13jMxo0b4ePjg48//hjr1q1Dr1690LJlS9y8eRMXL17E2bNnsXPnTlhYWOD+/fvw8fGBpaUlXn/9dVhYWODx48dITk7GuXPn4OrqqnErNlLHoKNakUqlmDlzJpKTk5Gamoq8vDy0aNECHTp0wJQpUzTuY7ho0SI0atQISUlJSE9PR0lJCT744AN4eXkBeLrM1KFDB6xevRqJiYkoKipC27ZtERgYiGnTpmksMzk4OOCXX37BvHnzcOzYMaSkpMDJyQnbtm3D5cuXsX//fq3PWY0bNw5NmjRBREQEduzYgaZNm6J3795Ys2YNEhISdHpT4EGDBuHnn3/G8uXL8dtvv2HPnj2QSCT44IMPMGPGDFhbW+ustpqo7OMFwNNZrDZBV3ZRSkREBAwMDPDhhx9W2PbLL7+ERCLBtm3b8P3336NFixZ4++23MXv2bMybN6/azymRSJCYmIg5c+bg+PHjSE1NhZOTE7Zu3QpDQ8Nyg659+/Y4evQoIiMjkZCQgLi4ODx+/Bht2rSBnZ0dFi9eDDc3NwBPz0XPnTsXycnJkMlkSExMhLGxMaysrPDNN99g7NixvK1ZFUQKhUJz3kwkAOPHj0dMTAzi4+PRr18/XZdDRDrCc3RUrymVSvz9998a23/77TfEx8fD1NQUffr00UFlRKQvuHRJ9VpJSQmcnJzw5ptvws7ODo0bN8alS5eQlJSERo0aYdmyZTxRT9TAcemS6jWlUomwsDCkpKTgzz//RGFhIcRiMVxcXPDJJ5+oznMQUcPFoCMiIkHjOToiIhI0Bh0REQkag46IiASNQfccuVyu6xLqnND6JLT+AMLrk9D6AwivT0LrT2UYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgsagIyIiQWPQERGRoDHoiIhI0Pg1PUSk5pN5S3A1v0hju42pMb6dM10HFRHVDoOOiNRczS9CarfxmjtOb3j5xRDVAS5dEhGRoDHoiIhI0Bh0REQkaAw6IiISNAYdEREJGoOOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoDDoiIhI0Bh0REQkag46IiASNQUdERILGoCMiIkFj0BERkaAx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgqazoCspKcGCBQvQpUsXmJmZoUuXLliwYAGePHmiaqNUKrFw4UI4ODjA3Nwc3t7euHjxotpxFAoFAgMDIZVKIZVKERgYCIVC8bK7Q0REekpnQbdy5UpERUUhPDwcMpkMixYtwoYNG7B8+XJVm1WrVmHNmjUIDw/HkSNHIJFIMGzYMNy7d0/VJiAgABkZGYiJiUFsbCwyMjIwYcIEXXSJiIj0UGNdPbFMJsOgQYPg5eUFALCysoKXlxd+//13AE9ncxEREQgJCYGPjw8AICIiAnZ2doiNjcW4ceOQmZmJw4cP4+DBg3B1dQUArFixAl5eXpDL5bCzs9NN54iISG/obEbn5uaGlJQUXL58GQBw6dIlJCcnY8CAAQCA7Oxs5OTkoF+/fqrHGBoawt3dHenp6QCehqWJiYkq5MqOa2xsrGpDREQNm85mdCEhISgsLISrqysMDAzw5MkTTJs2DQEBAQCAnJwcAIBEIlF7nEQiwa1btwAAubm5MDU1hUgkUu0XiURo3bo1cnNzX1JPiIhIn+ks6OLj47Fz505ERUXBwcEBZ8+exeeffw6pVAp/f39Vu2dDDHi6pPl8sD3v+TbPk8vlldZW1f76SGh9Elp/AP3pU/H94gq3a1OjvvSnLgmtT0LpT1WnqXQWdHPmzMHkyZMxfPhwAICTkxNu3LiBFStWwN/fH2ZmZgCeztosLCxUj8vLy1PN8tq0aYO8vDy1YFMqlcjPz9eYCT6rshdFiOf2hNYnofUH0K8+GRoZVri9ujXqU3/qitD6JLT+VEZn5+ju378PAwMDtW0GBgYoLS0F8PTiFDMzMyQlJan2P3jwAGlpaapzci4uLigsLIRMJlO1kclkKCoqUjtvR0REDZfOZnSDBg3CypUrYWVlBQcHB2RkZGDNmjUYNWoUgKdLksHBwVi2bBns7Oxga2uLpUuXwtjYGCNGjAAA2Nvbo3///pg6dSpWrVoFpVKJqVOnwtPTs8G8UyEiosrpLOgWL16Mr7/+Gp999hny8vJgZmaGMWPGYMaMGao2U6ZMQXFxMaZPnw6FQoGePXsiPj4ezZo1U7XZsGEDQkND4efnBwDw8vLC4sWLX3p/iIhIP+ks6Jo1a4ZFixZh0aJFFbYRiUQICwtDWFhYhW1atmyJyMjIF1EiEREJAO91SUREgsagIyIiQWPQERGRoDHoiIhI0Bh0REQkaAw6IiISNAYdEREJGoOOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoDDoiIhI0Bh0REQkag46IiASNQUdERILGoCMiIkFj0BERkaAx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgsagIyIiQWPQERGRoDHoiIhI0Bh0REQkaAw6IiISNAYdEREJGoOOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoOg26v//+G0FBQbCxsYGZmRlcXV2RkpKi2q9UKrFw4UI4ODjA3Nwc3t7euHjxotoxFAoFAgMDIZVKIZVKERgYCIVC8bK7QkREekpnQadQKODp6QmlUono6Gikp6dj8eLFkEgkqjarVq3CmjVrEB4ejiNHjkAikWDYsGG4d++eqk1AQAAyMjIQExOD2NhYZGRkYMKECbroEhER6aHGunrib7/9Fubm5li/fr1qm7W1teq/lUolIiIiEBISAh8fHwBAREQE7OzsEBsbi3HjxiEzMxOHDx/GwYMH4erqCgBYsWIFvLy8IJfLYWdn91L7RERE+kdnM7rExET07NkT48aNg62tLfr27YvIyEgolUoAQHZ2NnJyctCvXz/VYwwNDeHu7o709HQAgEwmg4mJiSrkAMDNzQ3GxsaqNkRE1LDpLOiuXbuGjRs3wtraGnFxcQgKCsLcuXOxYcMGAEBOTg4AqC1llv2em5sLAMjNzYWpqSlEIpFqv0gkQuvWrVVtiIioYdPZ0mVpaSm6d++OL7/8EgDQtWtXZGVlISoqCoGBgap2z4YY8HRJ8/lge97zbZ4nl8srra2q/fWR0PoktP4A+tOn4vvFFW7XpkZ96U9dElqfhNKfqk5T6SzozMzMYG9vr7atY8eO+PPPP1X7gaezNgsLC1WbvLw81SyvTZs2yMvLUws2pVKJ/Px8jZngsyp7UYR4bk9ofRJafwD96pOhkWGF26tboz71p64IrU9C609ldLZ06ebmhitXrqhtu3LlCiwtLQEAVlZWMDMzQ1JSkmr/gwcPkJaWpjon5+LigsLCQshkMlUbmUyGoqIitfN2RETUcOks6CZOnIiTJ09i6dKlyMrKwu7duxEZGYmAgAAAT5ckg4ODsXLlSiQkJODChQuYOHEijI2NMWLECACAvb09+vfvj6lTp+LkyZOQyWSYOnUqPD09G8w7FSIiqpzOli579OiB7du3Y968eViyZAksLCwwc+ZMVdABwJQpU1BcXIzp06dDoVCgZ8+eiI+PR7NmzVRtNmzYgNDQUPj5+QEAvLy8sHjx4pfeHyIi0k9aBV14eDiGDBkCR0fHcvdfvHgRCQkJCA0NrdbxPD094enpWeF+kUiEsLAwhIWFVdimZcuWiIyMrNbzERFRw6PV0uWiRYtw/vz5CvdfvHgR4eHhtS6KiIiortTpObrCwkK88sordXlIIiKiWqly6fLcuXM4e/as6ve0tDQ8efJEo51CocCmTZtga2tbtxUSERHVQpVBt2/fPtVypEgkwubNm7F58+Zy2zZr1kx1ZxMiIiJ9UGXQ+fv7o3///lAqlRg4cCA+//xzvPPOO2ptRCIRjIyMYGNjgyZNmrywYomIiLRVZdC1a9cO7dq1AwDs3bsX9vb2ld51hIiISJ9o9fGCvn37vqg6iIiIXgitPzB+9OhRbNmyBdeuXcOdO3dUX6tTRiQS4fTp03VWIBERUW1oFXQRERH44osv0Lp1a/Tq1QudOnV6UXURERHVCa2Cbs2aNejTpw/i4uJ40QkREdULWn1gPD8/H35+fgw5IiKqN7QKum7duuH69esvqhYiIqI6p1XQff311/jxxx9x7NixF1UPERFRndLqHN3ChQvRvHlz+Pr6wsbGBpaWljAwMFBrIxKJEB0dXadFEpHuXcm8BO8pX5W7z8bUGN/Omf5yCyKqJq2C7tKlSxCJRLCwsMDDhw81viEceBp0RCQ8xQZNkdptfPk7T/PWf6S/tAq6Z2/uTEREVB/U6df0EBER6RutZnQ3btyoVjtLS8saFUNERFTXtAq6Ll26VOsc3O3bt2tcEBERUV3SKui+++47jaArKSlBdnY2du7ciTZt2iAgIKBOCyQiIqoNrYJu9OjRFe4LCQlBv379UFhYWOuiiIiI6kqdXYxiYmKC0aNHY+3atXV1SCIiolqr06suX3nlFdy6dasuD0lERFQrdRZ0Z8+exbp162Bvb19XhyQiIqq1OrnqsqCgAHfv3oWJiQnWrFlTZ8URERHVllZB16dPH42gE4lEEIvF6NChA4YPHw6xWFynBRIREdWG1t8wTkREVJ/U6hzdvXv3cO/evbqqhYiIqM5pHXTXr1/HhAkT0KFDB1hZWcHKygodOnRAUFAQv5SViIj0jlZLl3K5HJ6enigoKMDbb78Ne3t7KJVKyOVyxMTE4JdffsGhQ4dga2v7ouolIiLSilZBN3fuXCiVSiQlJaFLly5q+86ePQsfHx/MnTsXP/zwQ50WSUREVFNaLV2mpKRgwoQJGiEHAJ07d8b48eORnJxcZ8URERHVllZB9+jRIzRv3rzC/S1atMCjR49qXRQREVFd0SroHB0dsWvXLhQXF2vse/jwIXbt2gVHR8c6K46IiKi2tDpH9+mnn+LDDz+Eh4cH/vOf/8DOzg4AcPnyZWzatAlyuRzbtm17IYUSERHVhFZBN3jwYERGRmLWrFmYMWOG6i4pSqUSZmZmiIyMhJeX1wsplIiIqCa0CjoAGDFiBHx9fXH69GnV5+akUim6deuGxo21PhwREdELVaNkaty4MXr16oVevXrVdT1ERER1qsqLUXJycvD6669j/vz5lbabP38+XFxckJeXV6NCli1bBrFYjOnTp6u2KZVKLFy4EA4ODjA3N4e3tzcuXryo9jiFQoHAwEBIpVJIpVIEBgZCoVDUqAYiIhKeKoNu3bp1uH37NkJCQiptN2XKFOTn52P9+vVaF3Hy5Els2bIFTk5OattXrVqFNWvWIDw8HEeOHIFEIsGwYcPU7q8ZEBCAjIwMxMTEIDY2FhkZGZgwYYLWNRARkTBVGXQ///wz/Pz80KxZs0rbNW/eHMOHD8eBAwe0KqCgoADjx4/H6tWr1b7iR6lUIiIiAiEhIfDx8YGjoyMiIiJQWFiI2NhYAEBmZiYOHz6MlStXwtXVFS4uLlixYgUOHToEuVyuVR1ERCRMVQbdH3/8AWdn52odzMnJCVlZWVoVUBZkb731ltr27Oxs5OTkoF+/fqpthoaGcHd3R3p6OgBAJpPBxMQErq6uqjZubm4wNjZWtSEiooatyotRRCIRSktLq3Ww0tLScr+BvCJbtmxBVlZWucudOTk5AACJRKK2XSKR4NatWwCA3NxcmJqaqj2nSCRC69atkZubW+HzVjXbE+JsUGh9Elp/AP3pU/F9zRtCAEBJScV/B4rvF2vUry/9qUtC65NQ+lP2me6KVBl0UqkUv//+O8aNG1flk506dQpSqbRahcnlcsybNw8HDhxAkyZNKmz3fHAqlUqNYHve822eV9mLIpfLq3zR6huh9Ulo/QH0q0+GRoblbjcwqHgByNDIUK1+fepPXRFan4TWn8pUuXTp6emJuLg4XL58udJ2ly9fRmxsLAYNGlStJ5bJZMjPz0c7KQJqAAAVrklEQVTv3r1hamoKU1NTpKamIioqCqampmjVqhUAaMzM8vLyVLO8Nm3aIC8vD0qlUrVfqVQiPz9fYyZIREQNU5VBN3nyZBgbG2PIkCGIjY3FkydP1PY/efIEsbGxGDp0KJo1a4bJkydX64m9vb1x/PhxJCcnq366d++O4cOHIzk5Gba2tjAzM0NSUpLqMQ8ePEBaWprqnJyLiwsKCwshk8lUbWQyGYqKitTO2xERUcNV5dJl69atERMTg9GjRyMwMBCffPIJbG1tYWJigsLCQly5cgUPHjxA27ZtsXPnTpiamlbricVisdpVlgBgZGSEli1bqm4MHRwcjGXLlsHOzg62trZYunQpjI2NMWLECACAvb09+vfvj6lTp2LVqlVQKpWYOnUqPD09G8yUnIiIKletO6N0794daWlp2Lx5Mw4ePIjMzEzcu3cPzZo1Q5cuXeDl5YWxY8eiRYsWdVrclClTUFxcjOnTp0OhUKBnz56Ij49X+6jDhg0bEBoaCj8/PwCAl5cXFi9eXKd1EBFR/VXtW4C1aNECISEhVX5wvDYSExPVfheJRAgLC0NYWFiFj2nZsiUiIyNfWE1ERFS/afV9dERERPUNg46IiASNQUdERILGoCMiIkFj0BERkaAx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgsagIyIiQWPQERGRoDHoiIhI0Bh0REQkaAw6IiISNAYdEREJGoOOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoDDoiIhI0Bh0REQkag46IiASNQUdERILGoCMiIkFj0BERkaAx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgsagIyIiQWus6wKI6OX7ZN4SXM0vKnef/NoNoNtLLojoBdLZjG758uXw8PCApaUlbGxsMHLkSFy4cEGtjVKpxMKFC+Hg4ABzc3N4e3vj4sWLam0UCgUCAwMhlUohlUoRGBgIhULxMrtCVO9czS9Carfx5f48eFKi6/KI6pTOgi4lJQX/+c9/cOjQISQkJKBx48bw9fXFnTt3VG1WrVqFNWvWIDw8HEeOHIFEIsGwYcNw7949VZuAgABkZGQgJiYGsbGxyMjIwIQJE3TRJSIi0kM6W7qMj49X+339+vWQSqU4ceIEvLy8oFQqERERgZCQEPj4+AAAIiIiYGdnh9jYWIwbNw6ZmZk4fPgwDh48CFdXVwDAihUr4OXlBblcDjs7u5feLyIi0i96czFKYWEhSktLIRaLAQDZ2dnIyclBv379VG0MDQ3h7u6O9PR0AIBMJoOJiYkq5ADAzc0NxsbGqjZERNSw6c3FKJ9//jk6d+4MFxcXAEBOTg4AQCKRqLWTSCS4desWACA3NxempqYQiUSq/SKRCK1bt0Zubm6FzyWXyyutpar99ZHQ+iS0/gAvt0/F94sr3FdSUqrV9rLjPV8/x0j/CaU/Va3e6UXQzZw5EydOnMDBgwdhYGCgtu/ZEAOeXqDyfLA97/k2z6vsRRHikqfQ+iS0/gAvv0+GRoYV7jMwKH+hp6LtZcd7tn6Okf4TWn8qo/Oly7CwMMTFxSEhIQHW1taq7WZmZgCgMTPLy8tTzfLatGmDvLw8KJVK1X6lUon8/HyNmSARETVMOg260NBQxMbGIiEhAR07dlTbZ2VlBTMzMyQlJam2PXjwAGlpaapzci4uLigsLIRMJlO1kclkKCoqUjtvR0REDZfOli6nTZuGXbt2Ydu2bRCLxapzcsbGxjAxMYFIJEJwcDCWLVsGOzs72NraYunSpTA2NsaIESMAAPb29ujfvz+mTp2KVatWQalUYurUqfD09GwwU3IiIqqczoIuKioKAFQfHSgTGhqKsLAwAMCUKVNQXFyM6dOnQ6FQoGfPnoiPj0ezZs1U7Tds2IDQ0FD4+fkBALy8vLB48eKX1AsiItJ3Ogu66ty9RCQSISwsTBV85WnZsiUiIyPrsjQiIhIQnV+MQkRE9CIx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI1BR0REgsagIyIiQWPQERGRoDHoiIhI0Bh0REQkaAw6IiISNAYdEREJGoOOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoDDoiIhI0Bh0REQkag46IiASNQUdERILGoCMiIkFrrOsCiKj+u5J5Cd5TvlL9Xny/GIZGhgAAG1NjfDtnuo4qI2LQEVEdKDZoitRu48vfeXrDyy2G6DlcuiQiIkFj0BERkaAx6IiISNAYdEREJGgMOiIiEjQGHRERCRqDjoiIBI2foyMSqE/mLcHV/KJy98mv3QC6veSCiHSEQUckUFfziyr8EHfzK1+85GqIdIdLl0REJGic0RHRC/X8fTCfxftg0ssgmKCLiorCt99+i5ycHDg4OGDhwoVwd3fXdVlEL1R9OA/H+2CSrgki6OLj4/H5559j2bJlcHNzQ1RUFN577z2cOHEClpaWui6PqEpfr9uCf56U/79jZbOe+n4errLZXm72FbSxstVqH2eIVB5BBN2aNWvwr3/9C2PGjAEALFmyBL/++is2bdqEL7/8UsfVkRBVNpOqyR/oS1dvIH/4N+U+5squzyoMA32ZtdVUZbO95le+gFzLfZW9VjUZF4DhKQQihUKh1HURtfHo0SO0bdsWGzduhK+vr2r7tGnTcOHCBezfv1+H1RERka7V+6su8/PzUVJSAolEorZdIpEgNzdXR1UREZG+qPdBV0YkEqn9rlQqNbYREVHDU++DztTUFAYGBhqzt7y8PI1ZHhERNTz1PuiaNGmCbt26ISkpSW17UlISXF1ddVQVERHpC0FcdTlp0iRMmDABPXv2hKurKzZt2oS///4b48aN03VpRESkY/V+RgcAfn5+WLhwIZYsWYI33ngDJ06cQHR0NKRSqarNhg0b4O7uDktLS1haWmLAgAE4dOhQpcc9f/48Bg8eDHNzc3Tq1Anh4eFQKvXnIlVt+5SdnQ2xWKzxc/jw4ZdYdfUtW7YMYrEY06dXfmm3vo9Tmer0R9/HaOHChRq1dezYsdLH6Pv4aNsnfR8jAPj7778RFBQEGxsbmJmZwdXVFSkpKZU+Rt/HqTYEMaMDgICAAAQEBFS4v127dpg7dy5sbGxQWlqKHTt2YPTo0Th69CicnZ012t+9exfDhg2Du7s7jhw5ArlcjkmTJsHIyAgff/zxi+xKtWnbpzJxcXFq+1u2bPkyytXKyZMnsWXLFjg5OVXarj6ME1D9/pTR5zGys7PDvn37VL8bGBhU2La+jI82fSqjr2OkUCjg6ekJNzc3REdHw9TUFNnZ2ZVes1BfxqmmBBN0VfH29lb7ffbs2di4cSNOnjxZbijExMSguLgYERERMDQ0hKOjIy5fvoy1a9di8uTJenFFp7Z9KtOqVSuYmZm96PJqrKCgAOPHj8fq1auxePHiStvWh3HSpj9l9HmMGjduXO3a6sP4ANr1qYy+jtG3334Lc3NzrF+/XrXN2tq60sfUl3GqKUEsXWqrpKQEcXFxKCoqgouLS7ltZDIZevfuDUNDQ9W2d955B7du3UJ2dvbLKrXaqtOnMh999BFsbW3h6emJPXv2vKQKqy8kJAQ+Pj546623qmxbH8ZJm/6U0ecxunbtGjp16oQuXbrg3//+N65du1Zh2/owPoB2fSqjr2OUmJiInj17Yty4cbC1tUXfvn0RGRlZ6TJkfRmnmmpQQXf+/Hm0b98ebdq0wdSpU7Ft27YKl5Jyc3PL/RB62T59oU2fTExMMH/+fGzevBkxMTF48803MW7cOOzateslV12xLVu2ICsrC198Ub37NOr7OGnbH30fo169emHt2rWIiYlR3UR94MCBuH37drnt9X18AO37pO9jdO3aNWzcuBHW1taIi4tDUFAQ5s6diw0bKr6Bdn0Yp9poMEuXwNN1+OTkZBQUFCAhIQHBwcHYt28fHB0dy21f3ofQy9uuS9r0ydTUVG29vXv37rh9+zZWrVqFkSNHvsyyyyWXyzFv3jwcOHAATZo0qfbj9HWcatIffR+jAQMGqP3eq1cvdOvWDT/++CMmT55c7mP0dXzKaNsnfR+j0tJSdO/eXXWf365duyIrKwtRUVEIDAys8HH6Pk610aBmdE2aNEGHDh1U/wg6d+6MtWvXltu2TZs25X4IHYBefRBdmz6Vp2fPnsjKynqBFVafTCZDfn4+evfuDVNTU5iamiI1NRVRUVEwNTXFw4cPNR6jz+NUk/6UR5/G6HkmJiZwcHCosD59Hp+KVNWn8ujTGJmZmcHe3l5tW8eOHfHnn39W+Jj6OE7aaFBB97zS0lI8evSo3H0uLi5IS0vDgwcPVNuSkpLQtm1bWFlZvawStVZZn8pz9uxZvTmh7u3tjePHjyM5OVn10717dwwfPhzJycnlzor0eZxq0p/y6NMYPe/BgweQy+UV1qfP41ORqvpUHn0aIzc3N1y5ckVt25UrVyr9yrL6OE7aaDBB99VXX+H48ePIzs7G+fPnMXfuXKSkpOC9994DAMydOxdDhw5VtR8xYgQMDQ0xceJEXLhwAQkJCVi5ciUmTpyoN1N5bfv0448/IiYmBpmZmZDL5Vi9enWVyxkvk1gshqOjo9qPkZERWrZsCUdHR4hEono1TjXpj76P0axZs5CSkoJr167hv//9L8aMGYP79+/jgw8+AFA//z/Stk/6PkYTJ07EyZMnsXTpUmRlZWH37t2IjIxU+/hVfRyn2mgw5+hycnIQGBiI3NxcNG/eHE5OToiNjcU777wD4OkHLP/44w9V+xYtWuCnn37CtGnT4OHhAbFYjEmTJlV4HkIXtO0TACxduhQ3btyAgYEBbGxs8N133+nFeYXqqo/jVJn6NkY3b95EQEAA8vPz0bp1a/Tq1Qu//PKL6uYM9XF8tO0ToN9j1KNHD2zfvh3z5s3DkiVLYGFhgZkzZ6oFXX0cp9qo999HR0REVJkGs3RJREQNE4OOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHREeiQwMBDdu3fXdRlVunr1KoYPHw6pVAqxWKw3NzQmKg+DjkhLo0aNgpmZGRQKRYVtZs6cCbFYjPPnz7/Eyl6eyZMn48yZM5g5cybWr18PV1dXXZdEVCEGHZGWRo4ciYcPHyIhIaHc/aWlpYiPj4eTk1O1v1G8Pnn06BHS09MxatQoBAUFYeTIkVV+sSeRLjHoiLTk5eWF5s2bIyYmptz9x44dw99//603t4Sqa/n5+SgtLUWLFi10XQpRtTDoiLTUtGlTDB06FKmpqbh586bG/ujoaDRq1AgjRoxQbdu6dSuGDBkCOzs7tGnTBr169cK3335b6bc+A0BWVlaF58AcHR3VvhcNABQKBWbOnAlnZ2dIJBI4Oztj3rx51f5Gi9TUVHh7e6Ndu3awsLDAsGHDcOrUKdX+BQsWoFOnTgCAr7/+GmKxGKamphUeb8uWLRCLxdi6dava9sjISIjFYkRHR1erLqLaaDA3dSaqS++//z62bduGuLg4tbB58OAB9u3bh759+6Jdu3aq7Rs2bECnTp0wcOBAGBoa4tdff8WcOXNw7969an/7eFXu378Pb29v/PXXXxg7diysra2RkZGBVatW4cqVKxph87xjx45h+PDhsLCwwIwZM/DkyRNs3rwZ3t7e2L9/P7p37w4fHx9IJBKEhobCx8cHgwcPRqNGFb9fHjNmDBITE/HFF1/grbfegpWVFa5evYqvvvoKQ4cOxfvvv18nfSeqDIOOqAbeeOMNWFhYICYmRi3oDh48iLt372r8AT906BCMjIxUvwcEBCA4OBjr1q3DjBkz8Morr9S6ptWrV+OPP/7Ab7/9Bjs7O9X2jh074vPPP4dMJoOLi0uFj585cyaaN2+Ow4cPq2ZpI0eOhKurK2bNmoXExER07twZrVq1QmhoKJydnau1PLt69Wr07t0bkyZNwu7duxEcHAwTExOsWLGi1n0mqg4uXRLVgEgkwogRI5CRkYHMzEzV9ujoaNXS5rPKQq6kpAQKhQL5+fl44403cO/ePVy9erVOatq9ezfc3d3RqlUr5Ofnq348PDwAPJ2xVeSvv/7CuXPnMHr0aLWlSEtLS/j5+SEtLQ13796tUV1mZmZYtmwZUlJSMGjQIMhkMqxcubLSJU+iusSgI6qhstlM2UUpCoUChw8fVl2s8qzU1FR4eXnB3Nwc1tbWsLGxwcSJEwEABQUFdVLP1atXcfjwYdjY2Kj9lF36/88//1T42OvXrwOA2kywjL29PUpLS/HXX3/VuLZhw4Zh8ODB+O9//4uRI0di8ODBNT4Wkba4dElUQ506dYKzszNiY2Mxa9Ys7N69G48ePdJYtrx69Sr8/PxgZ2eH8PBwtG/fHq+++ipOnTqFefPmobS0tMLnqOzbnUtKStR+Ly0thYeHB6ZMmVJu+/bt22vRu7p1584d1UUtcrkcT548QePG/PNDLwf/pRHVwsiRIzF79mzIZDJER0ejVatW6N+/v1qb/fv34+HDh4iOjla7QKU6S5ZisRiA5qyvuLgYubm5atusra1RVFSEt99+W+t+lH2btlwu19h3+fJlNGrUqFZBOW3aNNy5cwfz58/H7NmzsXz5csyYMaPGxyPSBpcuiWrhvffeQ6NGjbBixQqkpaXBz89P48KSsqsSn/0owYMHDxAVFVXl8Vu2bAmxWIzk5GS17VFRURofTfDz84NMJsPPP/+scZz79++jqKiowudp3749nJ2d8eOPP+LOnTuq7X/99Rfi4+PRu3dvjeXY6tqzZw/i4uIwa9YsfPzxx/joo4+wZMkSnDlzpkbHI9IWZ3REtWBubo4333wTBw4cAIByL5fv378/vvrqK7z33nsYO3YsHjx4gJ07d1Z76W7cuHFYsWIFJk+ejB49euDUqVNITU1Fy5Yt1dqFhITgl19+wQcffIBRo0ahe/fuePjwIeRyOX766Sfs3r270vtofvPNN/Dz80P//v3h7++PkpISbNq0CSUlJZg/f74Wr8r/y83Nxaeffqq66rLseY4ePYrg4GAcPXoUTZo0qdGxiaqLMzqiWiq7KMXa2rrcy/ft7e3xww8/oFGjRpgzZw4iIyPh7e2NL7/8slrHnzFjBsaOHYu9e/di9uzZ+Oeff7B7924YGhqqtTMyMsK+ffvw6aefIj09HTNnzsTSpUuRkZGBSZMmwcbGptLnefPNN7F7926Ym5sjPDwcy5Ytg62tLRITE9GjR49qvhrqQkJC8ODBA6xdu1Y1s23WrBnWrFmDixcv4ptvvqnRcYm0IVIoFJXfmoGIiKge44yOiIgEjUFHRESCxqAjIiJBY9AREZGgMeiIiEjQGHRERCRoDDoiIhI0Bh0REQkag46IiASNQUdERIL2fzVA5p73VA9oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0efbceb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(results_df['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of TPE Values'); plt.xlabel('Value of x'); plt.ylabel('Count');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed the values of x evaluated cluster much closer to the optimum! The algorithm spend much more time around the best value than searching the domain space. We can compare this distribution to that attained with the TPE algorithm on the uniform domain using a Kernel Density Estimate Plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0eee07cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(results_df['x'], label = 'Normal Domain')\n",
    "sns.kdeplot(tpe_results['x'], label = 'Uniform Domain')\n",
    "plt.legend(); plt.xlabel('Value of x'); plt.ylabel('Density'); plt.title('Comparison of Domain Choice using TPE');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lowest Value of the Objective Function = -219.8012 at x = 4.8782 found in 956 iterations.\n"
     ]
    }
   ],
   "source": [
    "print('Lowest Value of the Objective Function = {:.4f} at x = {:.4f} found in {:.0f} iterations.'.format(results_df['loss'].min(),\n",
    "                                                                             results_df.loc[results_df['loss'].idxmin()]['x'],\n",
    "                                                                             results_df.loc[results_df['loss'].idxmin()]['iteration']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well that definitely shows the value of choosing a good prior! When it comes to hyperparameter tuning, we often do not know ahead of time what values to concentrate around but we can try to use past experience or the work of others to inform our search spaces. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions\n",
    "\n",
    "In this notebook, we saw a basic implementation of Bayesian Model-Based optimization using Hyperopt. This requires four parts:\n",
    "\n",
    "1. Objective: what we want to minimize\n",
    "2. Domain: values of the parameters over which to minimize the objective\n",
    "3. Hyperparameter optimization function: how the surrogate function is built and the next values are proposed\n",
    "4. Trials consisting of score, parameters pairs\n",
    "\n",
    "The differences between random search and and Sequential Model-Based Optimization is clear: random search is _uninformed_ and therefore requires more trials to minimize the objective function. The Tree Parzen Estimator, an algorithm used for SMBO, spends more time choosing the next values, but overall requires fewer evaluations of the objective function because it is able to _reason_ about the next values to evaluate. Over many iterations, SMBO algorithms concentrate the search around the most promising values, yielding:\n",
    "\n",
    "* Lower scores on the objective function\n",
    "* Faster optimization\n",
    "\n",
    "Bayesian model-based optimiziation means construction a probability model $p(y | x)$ of the objective function and updating this model as more information is collected. As the number of evaluations increases, the model (also called a surrogate function) becomes a more accurate respresentation of the objective function and the algorithm spends more time evaluating promising values.\n",
    "\n",
    "\n",
    "This notebook showed a the basic implementation of Bayesian Model-Based optimization using Hyperopt, but already we can see how it has significant advantages over random or grid search based methods. In future notebooks we will explore using Bayesian model-based optimization on more complex problems, namely hyperparameter optimization of machine learning models. "
   ]
  }
 ],
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